The author introduces a minimal B-error algorithm for interative techniques in solving the matrix equation Ax+b=0 following the general concepts introduced by G. H. Golub and R. S. Varga (1961). (MR0468134 )
The authors provide various methods for the representation of a certain class of rational iterative functions. They present certain multistep schemes for the computation of the value of n-optimal iterative functions which have practical applications. (MR0474737)
This article contains three sufficient conditions for the convergence of Jacobi and Gauss-Seidel iterative solutions of systems of linear equations of the form Ax=b. These conditions rely on a special property of the matrix A defined in this work as `the sum criterion'. This property is not equivalent in the general case to the irreducibility of the matrix A. The results obtained are regarded primarily as a theoretical aid towards understanding the Gauss-Seidel method. Practical usefulness of these methods is minimal since generally we can list other more effective iterative methods. (MR0455316)
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